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DiffEq Network

Some results for the tests of differential modular structures in two networks with a minimum module size of m=5 are provided in Table 1 of the paper. More detailed tables are given below. The following table shows the results for various choices of m and &epsilon and also presents the value of the test statistic N and its corresponding p-value.

&epsilon&epsilon&epsilon&epsilon&epsilon&epsilon&epsilon&epsilon

m	N	p-value		m	N	p-value		m	N	p-value		m	N	p-value		m	N	p-value	m	N	p-value		m	N	p-value		m	N	p-value
1	.20	.640	.000		2	.20	.641	.000		3	.20	.641	.000		4	.20	.641	.000	5	.20	.641	.000		6	.20	.641	.000		7	.20	.641	.000	8	.20	.641	.000
1	.25	.862	.000		2	.25	.862	.000		3	.25	.862	.000		4	.25	.862	.000	5	.25	.862	.000		6	.25	.862	.000		7	.25	.862	.000	8	.25	.862	.000
1	.30	.910	.000		2	.30	.910	.000		3	.30	.910	.000		4	.30	.910	.000	5	.30	.910	.000		6	.30	.910	.000		7	.30	.910	.000	8	.30	.910	.000
1	.35	.919	.003		2	.35	.919	.001		3	.35	.919	.001		4	.35	.919	.002	5	.35	.919	.001		6	.35	.919	.001		7	.35	.919	.004	8	.35	.919	.007
1	.40	.954	.000		2	.40	.954	.000		3	.40	.954	.000		4	.40	.954	.001	5	.40	.965	.003		6	.40	.965	.004		7	.40	.965	.004	8	.40	.965	.009

As seen in the table, the value of the test statistic and the structure of the networks are sensitive to the selection of &epsilon but the results are similar for a wide range of choices of m. However, the result of the significance test is not affected by our choice of &epsilon for this analysis. Thus, regardless of how we define a module, the observed data supports the statement that the two networks have significantly different modular structures.